@Joey Allison Mold is fairly common in Arizona, once moisture is introduced it can take off pretty quick.Mold is also very treatable in most cases.

@John Underwood You could get a moisture reading in your crawl space to see if you have a problem that needs to be addressed.You might need a moisture barrier if you don't have one.

Getting rid of it is fairly easy:  stop the moisture intrusion including condensation and clean with bleach.

However from that list - the most concerning items are associated to appearance of mold (laundry wall room/ behind hall bath toilet) and identification of active moisture (laundry room ceiling / active moisture intrusion at lower wall of converted car port) in a few locations.

Just about any home built since about 1960/70 is designed to have functioning air circulation systems, and without circulating the air you are going to have mold, moisture, heat soak and other issues.

It compacts down and becomes water-impervious as opposed to dirt which can absorb moisture and could continue to cause moisture.

Roaches may like the moisture of a bathroom but they still need to eat. 

I have heard not to caulk around the batten so moisture can release Incase it gets trapped inside, but also heard caulk all around battens also to block and moisture going in.

I doubt that too; maybe it's just me but it puts me off to see carpet in a bathroom situation and in a place that may or may not have moisture issues - I'd just as soon see the floor painted and put down an area rug. 

There are some small cracks in the floor and most of the moisture was around those cracks kind of like water is coming up through the floor a little bit.